Upon activation by antigen, B cells form germinal centres where they clonally expand and introduce affinity‐enhancing mutations into their B‐cell receptor genes. Somatic mutagenesis and class switch recombination (CSR) in germinal centre B cells are initiated by the activation‐induced cytidine deaminase (AID). Upon germinal centre exit, B cells differentiate into antibody‐secreting plasma cells. Germinal centre maintenance and terminal fate choice require transcriptional reprogramming that associates with a substantial reconfiguration of DNA methylation patterns. Here we examine the role of ten‐eleven‐translocation (TET) proteins, enzymes that facilitate DNA demethylation and promote a permissive chromatin state by oxidizing 5‐methylcytosine, in antibody‐mediated immunity. Using a conditional gene ablation strategy, we show that TET2 and TET3 guide the transition of germinal centre B cells to antibody‐secreting plasma cells. Optimal AID expression requires TET function, and TET2 and TET3 double‐deficient germinal centre B cells show defects in CSR. However, TET2/TET3 double‐deficiency does not prevent the generation and selection of high‐affinity germinal centre B cells. Rather, combined TET2 and TET3 loss‐of‐function in germinal centre B cells favours C‐to‐T and G‐to‐A transition mutagenesis, a finding that may be of significance for understanding the aetiology of B‐cell lymphomas evolving in conditions of reduced TET function.